For a square matrix A, if

AB = BA = I

 

Then, B is the inverse of A

i.e. B = A −1

 

We will find inverse of a matrix by

Note: Since AB = BA = I

We can say B is the inverse of A.

i.e. B = A −1

 

We can also say,

A is the inverse of B

i.e. A = B −1

Thus, for inverse

We can write

  AA −1 = A −1 A = I

Where I is identity matrix of the same order as A

 

Let’s look at same properties of Inverse.

 

Properties of Inverse

  1. For  a matrix A,
    A −1 is unique, i.e., there is only one inverse of a matrix
  2. (A −1 ) −1   = A
  3. (k A)

    Note: This is different from

    (kA) T = k A T

  4. (A -1 ) T = (A T ) -1

  5. (A + B) -1 = A -1 + B -1

  6.  (AB) -1 = B -1 A -1

 

 

  1. Chapter 3 Class 12 Matrices
  2. Concept wise

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.